The difference is in the organization of the molecules which the atoms form, not in the atoms themselves.
The molecules themselves are not different, but they are part of larger structure (cells, unless you want to include viruses) that they are part of.
Although there is no commonly accepted definition of life, living things could be considered
self-sustaining, self replicating entities (when considered in the environment they are adapted to) that are capable of evolving by natural selection.
They use energy they obtain from their environment to maintain themselves and reproduce.
A technical comparison of this organization argument might be what is the difference between the atoms in a transistor in a functioning computer from those in:
a) a computer that is turned off
b) a computer that has been smashed to bits
c) a transistor that is just laying around on a lab bench
The atoms are part of larger entities that have properties based upon their higher level organization.
In all these cases, the atoms just do their atomistic things in the same way.